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Continuous versus Discrete Market Games

Author

Listed:
  • Alexandre Marino

    (CERMSEM)

  • Bernard De Meyer

    (CERMSEM)

Abstract

De Meyer and Moussa Saley [4] provide an endogenous justification for the appearance of Brownian Motion in Finance by modeling the strategic interaction between two asymmetrically informed market makers with a zero-sum repeated game with one-sided information. The crucial point of this justification is the appearance of the normal distribution in the asymptotic behavior of Vn(P)//n. In De Meyer and Moussa Saley’s model [4], agents can fix a price in a continuous space. In the real world however, the market compels the agents to post prices in a discrete set. The previous remark raises the following question: Does the normal density still appear in the asymptotic of Vn//n for the discrete market game? The main topic of this paper is to prove that for all discretization of the price set, Vn(P)//n converges uniformly to 0. Despite of this fact, we do not reject De Meyer, Moussa analysis: when the size of the discretization step is small as compared to n-1/2, the continuous market game is a good approximation of the discrete one.

Suggested Citation

  • Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1535
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d15/d1535.pdf
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    References listed on IDEAS

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    1. DE MEYER , Bernard, 1993. "Repeated Games and the Central Limit Theorem," CORE Discussion Papers 1993003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, January.
    3. Hadiza Moussa Saley & Bernard De Meyer, 2003. "On the strategic origin of Brownian motion in finance," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(2), pages 285-319.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. De Meyer, Bernard, 2010. "Price dynamics on a stock market with asymmetric information," Games and Economic Behavior, Elsevier, vol. 69(1), pages 42-71, May.
    2. repec:wsi:igtrxx:v:19:y:2017:i:01:n:s0219198916500171 is not listed on IDEAS
    3. Victor Domansky, 2007. "Repeated games with asymmetric information and random price fluctuations at finance markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 241-257, October.

    More about this item

    Keywords

    Insider trading; game of incomplete information; Brownian Motion;

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